Walmart Weekly Sales Forecasting: Model Comparison

Author

Machine Learning UTEC Homework

1 Objective

This report compares six forecasting approaches for weekly Walmart sales:

Local Linear Anomaly Model (Phase 1).
Bayesian Structural AR (Phase 2, full data).
Elastic Net anomaly baseline (Phase 3).
Random Forest anomaly baseline (Phase 4).
ETS anomaly baseline (Phase 5).
AdaBoost anomaly baseline (Phase 7).

Additionally, we include a Phase 1-lite diagnostic variant in the final comparison to show the impact of removing the extra exogenous variables from Local Linear.

Evaluation uses forward-chaining validation and weighted MAE (WMAE).

2 Data and Evaluation Setup

	Artifact	Value
0	Phase 1 OOF rows	154386
1	Phase 1-lite OOF rows	154386
2	Phase 2 OOF rows	47367
3	Elastic Net OOF rows	154386
4	Random Forest OOF rows	154386
5	ETS OOF rows	154386
6	AdaBoost OOF rows	154386

Validation metric:

\[ \text{WMAE} = \frac{\sum_i w_i \lvert y_i - \hat{y}_i \rvert}{\sum_i w_i}, \quad w_i = \begin{cases} 5, & \text{if holiday} \\ 1, & \text{otherwise} \end{cases} \]

3 Model 1: Local Linear Anomaly (Phase 1)

Local Linear is a weighted regression that learns a different local coefficient vector for each week-of-year neighborhood and each series. It is simple and interpretable, but sensitive to feature scaling, so standardization is applied before fitting.

3.1 Mathematical Formulation

For series \(s\) and target seasonal week \(w\):

\[ \hat{\beta}_{s,w} = \arg\min_{\beta} \sum_{i \in s} K_h\!\left(d(\text{week}_i,w)\right) \left(y_i - \beta_0 - x_i^\top \beta\right)^2 + \lambda \|\beta\|_2^2 \]

and recursive prediction:

\[ \hat{y}^{anom}_{t,s}=\beta_0 + x_{t,s}^\top \beta,\qquad \hat{y}_{t,s}=\hat{y}^{anom}_{t,s}+clim_{t,s} \]

3.2 Plain-Language Meaning of Terms

series s: one specific Store + Dept time series.
week_i and w: historical week index and target seasonal week where local fitting is centered.
K_h(d(.)): a weight that gives more importance to rows close in seasonal calendar (e.g., nearby weeks of year).
x_i: the input features for a row (lags, holiday flag, exogenous variables).
beta_0, beta: intercept and coefficients learned by local weighted regression.
lambda: regularization strength that shrinks coefficients to avoid unstable fits.
y^{anom}: anomaly target (real sales minus climatology baseline).
clim_{t,s}: baseline seasonal level added back to convert anomaly prediction to sales prediction.

3.3 Workflow

flowchart LR
  A[Read processed train/test parquet] --> B[Compute climatology per series/store/week]
  B --> C[Create anomalies and lag1/lag2]
  C --> D[Use pre-imputed exogenous features + fill lag defaults]
  D --> E[Standard-scale Phase 1 features]
  E --> F[Forward-chaining CV]
  F --> G[Fit local weighted ridge by series and seasonal week]
  G --> H[Recursive rollout on validation horizon]
  H --> I[OOF metrics and predictions]
  I --> J[Fit full train and forecast test]

3.4 Tuned Parameters and Effect

	Parameter	Value	How it works
0	kernel	tricube	Kernel shape over seasonal distance; controls ...
1	bandwidth	8	Neighborhood width in week-of-year units; larg...
2	min_samples	16	Minimum active samples to fit a local model; g...
3	ridge	0.0005	L2 regularization strength in weighted regress...
4	coef_clip	5.0	Post-fit coefficient clipping to prevent extre...
5	anom_clip_scale	2.0	Prediction clipping band around anomaly quanti...
6	lags	[1, 2]	Autoregressive inputs used in recursive foreca...
7	standard_scaler	True	Feature standardization before fitting local r...

{'train_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/train_feat.parquet',
 'test_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/test_feat.parquet',
 'output_dir': 'outputs',
 'kernel': 'tricube',
 'bandwidth': 8,
 'min_samples': 16,
 'ridge': 0.0005,
 'coef_clip': 5.0,
 'anom_clip_scale': 2.0,
 'n_folds': 4,
 'val_weeks': 13,
 'max_series': None,
 'use_interactions': False,
 'feature_mode': 'full',
 'lags': [1, 2],
 'interaction_cols': [],
 'exogenous_features': ['temp_anom',
  'fuel_anom',
  'MarkDown1',
  'MarkDown2',
  'MarkDown3',
  'MarkDown4',
  'MarkDown5',
  'CPI',
  'Unemployment'],
 'feature_cols': ['temp_anom',
  'fuel_anom',
  'MarkDown1',
  'MarkDown2',
  'MarkDown3',
  'MarkDown4',
  'MarkDown5',
  'CPI',
  'Unemployment',
  'sales_anom_lag1',
  'sales_anom_lag2',
  'is_holiday_int'],
 'standard_scaler': True}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse
0	1	2010-02-05	2011-10-28	2011-11-04	2012-01-27	2968.579714	3028.312165	6596.269740
1	2	2010-02-05	2012-01-27	2012-02-03	2012-04-27	8315.104990	8378.637596	16999.560174
2	3	2010-02-05	2012-04-27	2012-05-04	2012-07-27	9125.216805	9125.216805	17656.786189
3	4	2010-02-05	2012-07-27	2012-08-03	2012-10-26	8930.783748	8983.278528	17013.768782

wmae     7334.921314
mae      7378.861274
rmse    14566.596221
Name: 4, dtype: object

4 Model 1-lite: Local Linear Diagnostic Variant

Phase 1-lite keeps the same Local Linear method but removes the extra exogenous variables (MarkDown1-5, CPI, Unemployment) and uses only temp_anom, fuel_anom plus lags/holiday.

{'train_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/train_feat.parquet',
 'test_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/test_feat.parquet',
 'output_dir': 'outputs/phase1_local_linear_lite',
 'kernel': 'tricube',
 'bandwidth': 6,
 'min_samples': 16,
 'ridge': 0.0001,
 'coef_clip': 6.0,
 'anom_clip_scale': 2.0,
 'n_folds': 4,
 'val_weeks': 13,
 'max_series': None,
 'use_interactions': False,
 'feature_mode': 'lite',
 'lags': [1, 2],
 'interaction_cols': [],
 'exogenous_features': ['temp_anom', 'fuel_anom'],
 'feature_cols': ['temp_anom',
  'fuel_anom',
  'sales_anom_lag1',
  'sales_anom_lag2',
  'is_holiday_int'],
 'standard_scaler': True}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse
0	1	2010-02-05	2011-10-28	2011-11-04	2012-01-27	2468.567458	2271.802436	4955.291247
1	2	2010-02-05	2012-01-27	2012-02-03	2012-04-27	2199.682469	2196.184633	4485.720535
2	3	2010-02-05	2012-04-27	2012-05-04	2012-07-27	2028.753667	2028.753667	3948.262807
3	4	2010-02-05	2012-07-27	2012-08-03	2012-10-26	1947.742271	1923.235682	3954.874629

wmae    2161.186467
mae     2104.994105
rmse    4336.037305
Name: 4, dtype: object

5 Model 2: Bayesian Structural AR (Phase 2)

Structural AR combines hierarchical intercepts, autoregressive lags, exogenous drivers, and seasonal Fourier terms in one probabilistic model. It is designed to capture both shared structure and series-specific behavior.

5.1 Mathematical Formulation

In z-score space:

\[ y^{*}_{t,s} \sim \mathcal{N}(\mu_{t,s}, \sigma) \]

\[ \mu_{t,s} = \alpha_s + \beta_{lag}^\top lag_{t,s} + \beta_{exog}^\top exog_{t,s} + \beta_h h_{t,s} + \beta_{tr} trend_t + \beta_f^\top fourier_t \]

with hierarchical intercept:

\[ \alpha_s = \alpha_\mu + \alpha_\sigma z_s,\qquad z_s \sim \mathcal{N}(0,1) \]

5.2 Plain-Language Meaning of Terms

y*_{t,s}: normalized anomaly target for week t and series s.
mu_{t,s}: model mean prediction before adding random noise.
alpha_s: series-specific baseline level; each Store + Dept has its own intercept.
beta_lag, lag_{t,s}: coefficients and lag features that capture autoregressive behavior.
beta_exog, exog_{t,s}: effects of external drivers (temperature, markdown flags, CPI, unemployment, etc.).
beta_h h_{t,s}: holiday contribution.
beta_tr trend_t: long-run drift over time.
beta_f fourier_t: smooth yearly seasonal pattern via sine/cosine terms.
sigma: predictive noise level around the mean.

5.3 Workflow

flowchart LR
  A[Read train parquet] --> B[Compute climatology]
  B --> C[Create anomaly target and lag1/lag2]
  C --> D[Build trend and Fourier seasonal terms]
  D --> E[Fill exogenous NA from train medians]
  E --> F[Standardize lag/exogenous/trend variables]
  F --> G[Fit PyMC structural model via MAP]
  G --> H[Recursive probabilistic rollout by date]
  H --> I[Aggregate draws to mean/sd and intervals]
  I --> J[CV metrics and OOF outputs]

5.4 Tuned Parameters and Effect

	Parameter	Value	How it works
0	max_eval	1800	Maximum evaluations in MAP optimization; highe...
1	pred_draws	40	Number of stochastic recursive draws for predi...
2	fourier_order	3	Number of sine/cosine seasonal harmonics.
3	lag_orders	[1, 2]	Autoregressive lags used as structural predict...
4	sigma_clusters	0	Number of heteroskedastic noise clusters; 0 me...
5	exogenous_features	[temp_anom, fuel_anom, MarkDown1, MarkDown2, M...	External covariates entering the structural mean.

{'train_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/train_feat.parquet',
 'test_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/test_feat.parquet',
 'output_dir': 'outputs/phase2_structural_ar_full',
 'n_folds': 2,
 'val_weeks': 8,
 'max_eval': 1800,
 'random_seed': 8927,
 'pred_draws': 40,
 'fourier_order': 3,
 'sigma_clusters': 0,
 'max_series': None,
 'lag_orders': [1, 2],
 'exogenous_features': ['temp_anom',
  'fuel_anom',
  'MarkDown1',
  'MarkDown2',
  'MarkDown3',
  'MarkDown4',
  'MarkDown5',
  'CPI',
  'Unemployment'],
 'note': 'Structural AR model with hierarchical series intercept, trend, Fourier seasonality, and recursive validation.'}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse	runtime_sec
0	1	2010-02-05	2012-07-06	2012-07-13	2012-08-31	1858.615285	1858.615285	3605.180332	41.105816
1	2	2010-02-05	2012-08-31	2012-09-07	2012-10-26	1788.747710	1814.821572	3515.619512	27.821251

wmae           1823.681497
mae            1836.718428
rmse           3560.399922
runtime_sec      34.463533
Name: 2, dtype: object

6 Model 3: Elastic Net Anomaly Baseline (Phase 3)

Elastic Net is a linear model with combined L1/L2 regularization. It is a robust baseline for correlated tabular features and keeps an interpretable global linear structure.

6.1 Mathematical Formulation

\[ \hat{\beta} = \arg\min_{\beta} \frac{1}{2n}\|y - X\beta\|_2^2 + \alpha\left( \frac{1-l1\_ratio}{2}\|\beta\|_2^2 + l1\_ratio\|\beta\|_1 \right) \]

6.2 Plain-Language Meaning of Terms

X beta: linear combination of all features.
||y - X beta||^2: fit error term (how far predictions are from truth).
alpha: total regularization strength.
l1_ratio: balance between:
L1 penalty: pushes less-useful coefficients to exactly zero (feature selection behavior).
L2 penalty: smoothly shrinks coefficients for stability under correlated features.

6.3 Workflow

flowchart LR
  A[Read processed train/test parquet] --> B[Compute climatology and anomalies]
  B --> C[Create lag1/lag2 and calendar features]
  C --> D[Build exogenous feature matrix]
  D --> E[Use pre-imputed exogenous features + standard scaling]
  E --> F[Fit Elastic Net on train folds]
  F --> G[Recursive forecasting on validation horizon]
  G --> H[OOF metrics and predictions]
  H --> I[Fit full train and forecast test]

6.4 Tuned Parameters and Effect

	Parameter	Value	How it works
0	alpha	0.05	Overall regularization strength; larger values...
1	l1_ratio	0.3	Mix between L1 (sparsity) and L2 (stability).
2	max_iter	10000	Maximum coordinate-descent iterations for conv...
3	lags	[1, 2]	Lag features used in recursive setup.
4	features	[lag1, lag2, week_of_year, month, is_holiday_i...	Full tabular interface for model fitting.

{'train_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/train_feat.parquet',
 'test_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/test_feat.parquet',
 'output_dir': 'outputs/baselines/elastic_net',
 'n_folds': 4,
 'val_weeks': 13,
 'max_series': None,
 'alpha': 0.05,
 'l1_ratio': 0.3,
 'max_iter': 10000,
 'model': 'elastic_net',
 'target': 'sales_anom',
 'features': ['lag1',
  'lag2',
  'week_of_year',
  'month',
  'is_holiday_int',
  'temp_anom',
  'fuel_anom',
  'MarkDown1',
  'MarkDown2',
  'MarkDown3',
  'MarkDown4',
  'MarkDown5',
  'CPI',
  'Unemployment'],
 'lags': [1, 2]}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse	runtime_sec
0	1	2010-02-05	2011-10-28	2011-11-04	2012-01-27	2475.985274	2293.252765	4919.238999	0.866906
1	2	2010-02-05	2012-01-27	2012-02-03	2012-04-27	2207.708436	2224.478816	4446.840568	0.992713
2	3	2010-02-05	2012-04-27	2012-05-04	2012-07-27	1921.357797	1921.357797	3758.701811	0.948691
3	4	2010-02-05	2012-07-27	2012-08-03	2012-10-26	1805.900000	1774.649987	3661.513910	1.033331

wmae           2102.737877
mae            2053.434841
rmse           4196.573822
runtime_sec        0.96041
Name: 4, dtype: object

7 Model 4: Random Forest Anomaly Baseline (Phase 4)

Random Forest is an ensemble of decision trees trained on bootstrap samples. It captures nonlinear interactions with little feature engineering and is robust to mixed feature scales.

7.1 Mathematical Formulation

For \(B\) trees:

\[ \hat{y}(x)=\frac{1}{B}\sum_{b=1}^{B} T_b(x) \]

where each \(T_b\) is grown on a bootstrap sample and split candidates are randomized via max_features.

7.2 Plain-Language Meaning of Terms

T_b(x): prediction from tree b.
B: number of trees in the forest.
Final prediction is an average of trees, which reduces variance and improves robustness.
Bootstrap sampling means each tree sees a slightly different sampled training set.
Random split-feature selection (max_features) decorrelates trees, improving ensemble quality.

7.3 Workflow

flowchart LR
  A[Read processed train/test parquet] --> B[Compute climatology and anomalies]
  B --> C[Create lag1/lag2 + calendar + exogenous features]
  C --> D[Use pre-imputed exogenous features]
  D --> E[Train Random Forest on fold train]
  E --> F[Recursive multi-step rollout on fold validation]
  F --> G[OOF metrics and predictions]
  G --> H[Refit on full train and forecast test]

7.4 Tuned Parameters and Effect

	Parameter	Value	How it works
0	n_estimators	160	Number of trees; larger reduces variance but i...
1	max_depth	22	Maximum tree depth; controls model complexity.
2	min_samples_leaf	1	Minimum samples per leaf; regularizes tree par...
3	max_features	sqrt	Feature subset size considered at each split.
4	lags	[1, 2]	Autoregressive lag features used recursively.

{'train_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/train_feat.parquet',
 'test_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/test_feat.parquet',
 'output_dir': 'outputs/baselines/random_forest',
 'n_folds': 4,
 'val_weeks': 13,
 'max_series': None,
 'n_estimators': 160,
 'max_depth': 22,
 'min_samples_leaf': 1,
 'max_features': 'sqrt',
 'model': 'random_forest',
 'target': 'sales_anom',
 'features': ['lag1',
  'lag2',
  'week_of_year',
  'month',
  'is_holiday_int',
  'temp_anom',
  'fuel_anom',
  'MarkDown1',
  'MarkDown2',
  'MarkDown3',
  'MarkDown4',
  'MarkDown5',
  'CPI',
  'Unemployment'],
 'lags': [1, 2]}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse	runtime_sec
0	1	2010-02-05	2011-10-28	2011-11-04	2012-01-27	2448.471873	2248.049927	4908.325535	3.726079
1	2	2010-02-05	2012-01-27	2012-02-03	2012-04-27	2144.002646	2157.122843	4413.152265	4.437882
2	3	2010-02-05	2012-04-27	2012-05-04	2012-07-27	1915.995788	1915.995788	3650.625149	4.724520
3	4	2010-02-05	2012-07-27	2012-08-03	2012-10-26	1679.902840	1664.795344	3444.058588	5.243644

wmae           2047.093287
mae            1996.490976
rmse           4104.040384
runtime_sec       4.533031
Name: 4, dtype: object

8 Model 5: ETS Anomaly Baseline (Phase 5)

ETS here is used on residual anomalies after removing an exogenous linear component. This hybrid keeps classical exponential smoothing dynamics while allowing external regressors to explain systematic variation.

8.1 Mathematical Formulation

Exogenous residual decomposition:

\[ y^{anom}_{t,s}=g(x_{t,s}) + r_{t,s},\qquad g(\cdot)\text{ from Ridge regression} \]

Residual component \(r_{t,s}\) is modeled by ETS:

\[ r_{t,s} = \ell_{t-1,s}+b_{t-1,s}+s_{t-m,s}+\varepsilon_{t,s} \]

and final forecast:

\[ \hat{y}_{t,s}=clim_{t,s}+\hat{g}(x_{t,s})+\hat{r}_{t,s} \]

8.2 Plain-Language Explanation (What ETS Is)

ETS stands for Error, Trend, Seasonality. It is a classical time-series model that keeps three internal states and updates them week by week:

level: the current baseline sales level for the series.
trend: the direction/slope (increasing or decreasing behavior).
seasonality: repeating seasonal pattern (here around yearly weekly cycle).

In this project we first predict the anomaly using exogenous variables (g(x)), then ETS models the remaining residual pattern (r). The final prediction is:

exogenous part
plus ETS residual dynamics
plus climatology baseline to return to sales scale.

8.3 Plain-Language Meaning of Terms

y^{anom}: anomaly sales target.
g(x): exogenous linear predictor (Ridge) from external variables.
r_{t,s}: residual anomaly after removing exogenous part.
ell: level state.
b: trend state.
s: seasonal state.
epsilon: random error term.

8.4 Workflow

flowchart LR
  A[Read train/test parquet] --> B[Compute climatology and anomalies]
  B --> C[Fit exogenous Ridge on anomaly target]
  C --> D[Compute residual anomaly = target - exogenous prediction]
  D --> E[Fit per-series ETS on residuals with fallback candidates]
  E --> F[Recursive fold forecasting by series]
  F --> G[Add exogenous component + climatology back]
  G --> H[OOF metrics and test forecasts]

8.5 Tuned Parameters and Effect

	Parameter	Value	How it works
0	seasonal_periods	52	Season length used by ETS seasonal state.
1	exog_alpha	1.0	Ridge penalty for exogenous linear component.
2	exogenous_features	[temp_anom, fuel_anom, MarkDown1, MarkDown2, M...	Regressors used before ETS residual modeling.
3	n_folds	4	Forward-chaining fold count.
4	val_weeks	13	Validation horizon length per fold.

{'train_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/train_feat.parquet',
 'test_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/test_feat.parquet',
 'output_dir': 'outputs/baselines/ets',
 'n_folds': 4,
 'val_weeks': 13,
 'max_series': None,
 'seasonal_periods': 52,
 'exog_alpha': 1.0,
 'model': 'ets',
 'target': 'sales_anom (via exogenous + ETS residual)',
 'exogenous_features': ['temp_anom',
  'fuel_anom',
  'MarkDown1',
  'MarkDown2',
  'MarkDown3',
  'MarkDown4',
  'MarkDown5',
  'CPI',
  'Unemployment'],
 'cv_mode_counts': {'level': 10550,
  'level-trend': 1847,
  'global-fallback': 77,
  'last-value-fallback': 51,
  'level-seasonal': 2},
 'test_mode_counts': {'level': 2719,
  'level-trend': 411,
  'level-seasonal': 8,
  'global-fallback': 11,
  'last-value-fallback': 20}}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse	runtime_sec
0	1	2010-02-05	2011-10-28	2011-11-04	2012-01-27	2350.210994	2193.430784	4866.046429	35.455143
1	2	2010-02-05	2012-01-27	2012-02-03	2012-04-27	2036.512652	2050.230681	4093.131724	323.797742
2	3	2010-02-05	2012-04-27	2012-05-04	2012-07-27	1540.042559	1540.042559	3030.647527	334.129346
3	4	2010-02-05	2012-07-27	2012-08-03	2012-10-26	1442.141483	1444.279579	2974.737166	515.819794

wmae           1842.226922
mae            1806.995901
rmse           3741.140712
runtime_sec     302.300506
Name: 4, dtype: object

9 Model 6: AdaBoost Anomaly Baseline (Phase 7)

AdaBoost builds an additive ensemble of shallow trees, where each stage focuses more on difficult residual patterns from previous stages.

9.1 Mathematical Formulation

With base learners \(h_m\):

\[ F_M(x)=\sum_{m=1}^{M}\nu_m h_m(x) \]

where stage weights depend on chosen boosting loss and learning rate. In practice here, \(h_m\) are depth-limited regression trees.

9.2 Plain-Language Meaning of Terms

h_m(x): base learner at stage m (small regression tree).
nu_m: effective contribution of stage m to the final prediction.
M: number of boosting stages.
learning_rate: shrinkage factor that controls how aggressively each stage updates the model.
Boosting logic: each new tree focuses more on errors made by previous trees.

9.3 Workflow

flowchart LR
  A[Read processed train/test parquet] --> B[Compute climatology and anomaly target]
  B --> C[Create lag1/lag2 + calendar + exogenous features]
  C --> D[Use pre-imputed exogenous features]
  D --> E[Train AdaBoost regressor on fold train]
  E --> F[Recursive validation rollout]
  F --> G[OOF metrics and predictions]
  G --> H[Refit on full train and produce test forecasts]

9.4 Tuned Parameters and Effect

	Parameter	Value	How it works
0	n_estimators	400	Number of boosting stages.
1	learning_rate	0.02	Shrinkage per stage; smaller needs more estima...
2	max_depth	3	Depth of each base regression tree.
3	loss	square	Boosting loss that controls how hard examples ...
4	lags	[1, 2]	Autoregressive lag inputs for recursive foreca...

{'train_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/train_feat.parquet',
 'test_path': '/home/ppalacios/Documents/Regression_Challenge_3-Walmart/walmart-recruiting-store-sales-forecasting/data/3.processed/test_feat.parquet',
 'output_dir': 'outputs/baselines/adaboost',
 'n_folds': 4,
 'val_weeks': 13,
 'max_series': None,
 'n_estimators': 400,
 'learning_rate': 0.02,
 'max_depth': 3,
 'loss': 'square',
 'model': 'adaboost',
 'target': 'sales_anom',
 'features': ['lag1',
  'lag2',
  'week_of_year',
  'month',
  'is_holiday_int',
  'temp_anom',
  'fuel_anom',
  'MarkDown1',
  'MarkDown2',
  'MarkDown3',
  'MarkDown4',
  'MarkDown5',
  'CPI',
  'Unemployment'],
 'lags': [1, 2]}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse	runtime_sec
0	1	2010-02-05	2011-10-28	2011-11-04	2012-01-27	2484.325260	2278.419476	4927.184916	122.836803
1	2	2010-02-05	2012-01-27	2012-02-03	2012-04-27	2194.568601	2196.823531	4386.792010	164.614742
2	3	2010-02-05	2012-04-27	2012-05-04	2012-07-27	2001.002929	2001.002929	3888.068247	188.977189
3	4	2010-02-05	2012-07-27	2012-08-03	2012-10-26	1814.980098	1795.546030	3696.075311	220.460867

wmae           2123.719222
mae            2067.947992
rmse           4224.530121
runtime_sec       174.2224
Name: 4, dtype: object

10 Final Comparative

10.1 Full-Data Comparison (Phases 1, 2, 3, 4, 5, 7 + Phase 1-lite Diagnostic)

	Model	Mean WMAE	Mean MAE	Mean RMSE
0	Structural AR (Phase 2)	1823.681497	1836.718428	3560.399922
1	ETS (Phase 5)	1842.226922	1806.995901	3741.140712
2	Random Forest (Phase 4)	2047.093287	1996.490976	4104.040384
3	Elastic Net (Phase 3)	2102.737877	2053.434841	4196.573822
4	AdaBoost (Phase 7)	2123.719222	2067.947992	4224.530121
5	Local Linear Lite (Phase 1-lite)	2161.186467	2104.994105	4336.037305
6	Local Linear Anomaly (Phase 1)	7334.921314	7378.861274	14566.596221

11 Conclusion

Full-data comparison is now apples-to-apples for all six models.
All tabular baselines share the same anomaly feature interface with lag1 and lag2.
The ranking table above is the reference for selecting the best model in this run.